I just (re-)tested it in Firefox 20.0 and Chrome 26.0.1410.43 and the icon selector still looks fine on my end.

Maybe there's another factor at work here, like a plugin conflict. Try temporarily deactivating other plugins and see if it fixes the problem. Also, check your JavaScript console for error messages while on the menu editor page.

Do you have any web development experience? Maybe you could try looking at the selection box in Firefox dev tools (i.e. "Inspect element") and see if you can figure out why the box contents get pushed down to the bottom of the page like that. I'm guessing that the upper-left corner is in the right place, but the element height is messed up for some reason.

Those inline styles are set by the $.position() utility function that I use to position the selection box below the icon button. Sounds like it produces incorrect results in your case. Maybe an old version of jQuery / jQuery UI is being loaded for some reason (e.g. failed upgrade)?

Interestingly, on my sites the "top" property is always negative. For example: "position: relative; top: -770px; left: 119px;". What happens if you flip the sign instead of changing it to "position: absolute"?

Lets see if setting position to absolute in the stylesheet helps fix the problem. As far as I can tell, jQuery will not change it to relative if it is already explicitly specified, and everything still seems to work fine on the test site.